This is happening not because of any fault in TrainSplit's website, but because of anticompetitive, incorrect, and frankly probably illegal discounting by LNER.
LNER and some other long-distance operators have a system whereby they sell [Super] Off-Peak Single tickets at half the price of the equivalent Return, provided you are booking a return journey - but only when booking online, and the appendix (Online) is added to the ticket name to signify the difference. So this might be useful for someone who can commit to a specific train and get an Advance on it in one direction, but who need the flexibility of a walk-up ticket in the other direction. Ordinarily, such Singles are usually priced only £1 or so below the equivalent Return, so as you can see, this is a very good offer.
Unfortunately, where LNER go wrong is in how they sell this ticket on their frankly incompetent website. Despite Virgin Trains East Coast having introduced their new website several years ago, several key issues remain. One of them is the fact that the website is unable to deal with the concept of forcing you to buy a return journey in order to get a [Super] Off-Peak Single (Online) ticket. This therefore means that they have implemented a "workaround" hack whereby they will instead sell you an ordinary [Super] Off-Peak Single, but 50% discounted (so actually slightly less than the 'correct' price of a [Super] Off-Peak Single (Online)).
This being a hack, there are some side effects - and one of them is the fact that it will sell you the 50% discounted ticket even where you are only booking a one-way journey. Another is the fact that you can only buy it if the itinerary contains solely LNER services. And, as they are selling the ticket at a discount (as if it were a promotional discount), you are unable to get a Railcard discount as well as the 50% discount, and therefore if you add a Railcard the ticket will get more expensive! Every other journey planner seems to handle this whole situation just fine - it's only LNER's rubbish website that has these limitations.
Of course, for the customer themselves, they are, in most cases, going to pay less if they use LNER's website. But this is an unfair advantage that LNER are offering merely because their website is so incompetently built. However, as other websites are able to sell the [Super] Off-Peak Single (Online) fares correctly, including with a Railcard discount, then in certain circumstances it may be cheapest to buy such a fare in the direction you wish to use it, and then to buy a very cheap Advance ticket for some arbitrary date in the future. This works best where you are on a route with several operators - so it may still be cheapest to split tickets at Doncaster, for example.
I agree that this is a wholly unsatisfactory situation, but what TrainSplit are saying is not wrong - if you turned up to the station on the day, you would pay £8.20 more as you would be sold a through ticket, plus in any case you would not get a [Super] Off-Peak Single (Online) ticket from a ticket machine or ticket office. However, LNER's incompetent website means they are undercutting other retailers, who, in good faith, say they are offering the lowest price.
So, really, who you ought to be complaining to is LNER.
